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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2013, Volume 19, Number 3, Pages 104–112
(Mi timm967)
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This article is cited in 3 scientific papers (total in 3 papers)
Asymptotic estimates for a solution of a singular perturbation optimal control problem on a closed interval under geometric constraints
A. R. Danilinab, N. S. Korobitsynab a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
b Ural Federal University named after B. N. Yeltsin
Abstract:
An optimal control problem is considered for solutions of a boundary value problem for a second-order ordinary differential equation on a closed interval with a small parameter at the second derivative. The control is scalar and satisfies geometric constraints. General theorems on approximation are obtained. Two leading terms of an asymptotic expansion of the solution are constructed and an error estimate is obtained for these approximations.
Keywords:
optimal control, time-optimal problem, asymptotic expansion, singular perturbation problems, small parameter.
Received: 21.03.2013
Citation:
A. R. Danilin, N. S. Korobitsyna, “Asymptotic estimates for a solution of a singular perturbation optimal control problem on a closed interval under geometric constraints”, Trudy Inst. Mat. i Mekh. UrO RAN, 19, no. 3, 2013, 104–112; Proc. Steklov Inst. Math. (Suppl.), 285, suppl. 1 (2014), S58–S67
Linking options:
https://www.mathnet.ru/eng/timm967 https://www.mathnet.ru/eng/timm/v19/i3/p104
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Abstract page: | 383 | Full-text PDF : | 109 | References: | 86 | First page: | 4 |
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